•Temperature •Thermal Expansion •Ideal Gas Law •Kinetic Theory •Heat •Heat Transfer •Phase Changes •Specific Heat •Calorimetry Zeroeth Law
• Two systems individually in thermal equilibrium with a third system (such as a thermometer) are in thermal equilibrium with each other. • That is, there is no flow of heat within a system in thermal equilibrium 1st Law of Thermo • The change of internal energy of a system due to a temperature or phase change is given by (next chapter): Temperature Change: Q = mcΔT Phase Change: Q = mL
• Q is positive when the system GAINS heat and negative when it LOSES heat. 2nd Law of Thermo
• Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. • Heat flows from hot to cold. • Alternative: Irreversible processes must have an increase in Entropy; Reversible processes have no change in Entropy. • Entropy is a measure of disorder in a system 3rd Law of Thermo
It is not possible to lower the temperature of any system to absolute zero. Absolute Zero
• In a constant volume thermometer, readings are virtually independent of the gas used • If the lines for various gases are extended, the pressure is always zero when the temperature is –273.15o C • This temperature is called absolute zero Absolute Temperature Scale
• Absolute zero is used as the basis of the absolute temperature scale • The size of the degree on the absolute scale is the same as the size of the degree on the Celsius scale • To convert:
TC = T –273.15 Absolute Temperature Scale, K • The absolute temperature scale is based on two fixed points – Adopted by in 1954 by the International Committee on Weights and Measures – One point is absolute zero – The other point is the triple point of water • This is the combination of temperature and pressure where ice, water, and steam can all coexist Phase Change: Triple Point
A temperature and pressure at which all three phases exist in equilibrium.
Lines of equilibrium Freezing-Melting Evaporation -Condensation
Sublimation Temperature is measured by a thermometer. Kelvin is the Absolute Scale.
9 TF()oo= TC ()32+ 5
5 TC()oo=−⎡ TF ()32⎤ 9 ⎣ ⎦
TK( )=+ T (o C ) 273.15
What is "room temperature" (68 degrees F) in Celsius and Kelvin?
5 TC()oo=−⎡ TF ()32⎤ 9 ⎣ ⎦ 5 =−⎡ o68 32⎤ = 20oC 9 ⎣ ⎦
TK( )=+ T (o C ) 273.15
= 293.15K
Do book quiz 2! 30 is HOT. 20 is NICE. 10 is CHILLY. Zero is ICE! http://hyperphysics.phy-astr.gsu.edu/Hbase/kinetic/pcokem.html#c1 Thermal Expansion: Linear
ΔL =ΔαLT0
Coefficients determined experimentally! Thermal Expansion: Volume
ΔVVT=Δβ 0
β ~ 3α Thermal Expansion: Linear Thermal Expansion: Linear
The coefficient of linear expansion of steel is 12 x 10-6/°C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would these rails change between a cold day when the temperature is -10 °C and a hot day at 30 °C?
ΔLLT=Δα 0 Δ=Lx(12 10−63 /ooo CmC )(10 )(30−− ( 10 C )) ΔL = .48m Thermal Expansion: Linear
ΔLLT=Δα 0 What change in temperature is needed to fill the gap, 1.3 x 10 -3 m?
−60−− 1 60− 1 ααbrass ==19xC 10 AL 23 xC 10
−3 Δ+Δ=LbrassLxm Al 1.3 10
−3 1.3xm 10 o Δ=TC=1121 ααbrassLL brass+ Al Al Thermal Expansion
When the temperature of a metal ring increases, does the hole become larger? Smaller? Or stay same?
Circle Expansion
The coefficient of linear expansion of aluminum is 23 x 10-6/C°. A circular hole in an aluminum plate is 2.725 cm in diameter at 0°C. What is the diameter of the hole if the temperature of the plate is raised to 100°C?
Δ=LLTα 0 Δ = (23xC 10−6 /oo )(2.725 cmC )100 = 6.3xcm 10−3 dcm= 2.731 Fluids: Liquids & Gases
•Fluids are substances that are free to flow. •Atoms and molecules are free to move. •They take the shape of their containers. •Cannot withstand or exert shearing forces.
Liquids: Incompressible (density constant) Gases: Compressible (density depends on pressure)
Parameters to describe Fluids: Density: ρ = mass/volume Pressure: P = Force/Area
[P] = N/m2 = 1 Pascal (Pa) Liquid Units There are 1000 liters in 1 cubic meter! 1 liter = 10-3 m3 = 103 cm3
1 liter of water has a mass of 1 kg and a weight of 9.8N.
1kg 1000 kg ρ == H2 0 liter m3 m ρ = Density V mV= ρ • Density of water @4°C: 3 3 ρwater = 1g/cm = 1000 kg/m = 1kg/liter
• Density of air @ 0°C: -3 3 3 ρAir = 1.29x10 g/cm = 1.29 kg/m Density depends on temperature! Most substances EXPAND upon heating. How does that change their densities? m ρ = REDUCES DENSITY! V Water: The Exception
3 • Water @4°C: ρwater =1000 kg/m 3 • Ice @ 0°C: ρice = 917 kg/m
Note: The graph is for ice water only. Ice is not on the graph! Thermal Expansion: Water
Water Expands when it cools below 4 °C ! Thus, the solid state is less dense than the liquid state: Thermometer, Liquid in Glass
• A common type of thermometer is a liquid-in-glass • The material in the capillary tube expands as it is heated • The liquid is usually mercury or alcohol Pressure in a fluid is due to the weight of a fluid. Force P = Area mg ()ρV g = = A A ()ρ Ah g = A P = ρgh Pressure depends on Depth! Pressure Acts ONLY Perpendicularly to the Surface
Pressure depends on depth. Pressure IN a Fluid
•Is due to the weight of the fluid above you •Depends on Depth and Density Only •Does NOT depend on how much water is present •Acts perpendicular to surfaces (no shearing) •Pressure’s add •At a particular depth, pressure is exerted equally in ALL directions including sideways (empirical fact) The Atmosphere
At sea level, the atmosphere has a density of about 1.29 kg/m3. The average density up to 120 km is about 8.59 x10-2 kg/m3. The Atmosphere 5 A square meter 1atm== 1.013 x 10 Pa 14.7 psi extending up through the atmosphere has a mass of about 10,000 kg and a weight of about 100,000 N. 1 N/m2 is a Pascal. Measuring Pressure 1atm= 1.013 x 105 Pa Why is the pressure at X equal to atmospheric pressure? Because if it didn’t, the mercury would P = ρgh be pushed out of the dish!
P = ρmercury gh P h = ρmercury =13.6ρwater ρmercury g 3 ρwater =1000kg / m 101,300Nm / 2 h = 13,600kg / m32 x 9.8 m / s hmm= 760 Measuring Pressure
Can a barometer be made with Water instead of Mercury?
P = ρwater gh P h = ρwater g
ρmercury =13.6ρwater 101,300Nm / 2 h = ρ =1000kg / m3 1000kg / m32 x 9.8 m / s water
hm=10.3
(Notice: 10.3m is just 13.6 x 760mm!) Barometers Measuring Air Pressure Fluid in the tube adjusts until the weight of the fluid column balances the atmospheric force exerted on the reservoir.
10.3m
Not to Scale!!!
Mercury Barometer Water Barometer 1atm= 1.013 x 105 Pa = 760mm Absolute vs. Gauge Pressure
Absolute Pressure: P = Pgh0 + ρ
Guage Pressure: P0 = ρgh
• Guage pressure is what you measure in your tires • Absoulte pressure is the pressure at B and is what is used in PV = nRT Why does the water stop when the top is closed?
Pressure is greater in the fluid at the spout due to weight of water so water flows. Hand covers top and water keeps flowing until the pressure is reduced to 1 atm by increasing volume of air above the fluid just like with a closed barometer! The absolute Pressure P of an ideal gas is directly proportional to the absolute (Kelvin) temperature T and the number of moles n of the gas and inversely proportional to the volume V of the gas: P V = nRT n = # moles R = 8.31 J/(mol-K) Universal Gas Constant P V = nRT
n = # moles R = 8.31 J/(mol-K) Universal Gas Constant
Note: PV is units of Energy! Atomic Units The Basics
•Atomic Number: # protons •Atomic Mass: # atomic mass units (u) •Atomic Mass Unit: 1/12 mass of C-12 atom • amu = u = 1.66 x 10-27 kg •Atomic Mass of C = 12.011u (1% is C-13) •Mass of 1 C = (12.011u) (1.66 x 10-27 kg/u) Moles and Avogadro’s Number 23 -1 NA= 6.022 x 10 mol •Mole (mol) = # atoms or molecules (particles) as are in 12 grams of Carbon-12: 1 mole = 6.022 x 1023 particles
• Avogadro’s Number: the number of particles in 23 -1 one mole: NA= 6.022 x 10 mol •# moles n contained in a sample of N particles:
n = N/ NA • # particles in a sample is: N = n NA More on Moles
The mass / mol for any substance has the same numerical value as its atomic mass: mass/mol C-12 = 12 g / mol mass/mol Li = 6.941 g / mol n = mass / (mass/mole) = mass / atomic mass
n = mass / atomic mass Q: How many moles are in 1 kg of Sodium?
mass/mole = atomic mass Na: 22.9898 g / mol n = mass / (mass/mole) = 1000 g / (22.9898g/mol) = 43.5 moles Q: How many atoms in 1 kg of Sodium?
# particles in a sample is: N = n NA N = (43.5mol) 6.022 x 1023 mol-1 = 2.62 x 1025 atoms P V = nRT n = # moles R = 8.31 J/(mol-K) Universal Gas Constant
PV = Nkt N= # particles k =1.38 x 10-23 J/K Boltzmann’s Constant
Note: PV is units of Energy! • The only interaction between particles are elastic collisions (no sticky - no loss of KE) • This requires LOW DENSITY • Excellent Approximation for O, N, Ar, CO2 @ room temperature and pressures • “State” is described by the Ideal Gas Law • Non “Ideal” are Van der Waals gases Ideal Gas Problem An ideal gas with a fixed number of molecules is maintained at a constant pressure. At 30.0 °C, the volume of the gas is 1.50 m3. What is the volume of the gas when the temperature is increased to 75.0 °C? PVnRT= VT 11= 11= PVnRT22= VT22
T2 33348K VV21= ==1.5mm 1.72 T1 303K Hot Question Suppose you apply a flame to 1 liter of water for a certain time and its temperature rises by 10 degrees C. If you apply the same flame for the same time to 2 liters of water, by how much will its temperature rise? a) 1 degree b) 5 degrees c) 10 degrees d) zero degrees